Biorthogonal Expansion of Non-Symmetric Jack Functions
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We find a biorthogonal expansion of the Cayley transform of the non-symmetric Jack functions in terms of the non-symmetric Jack polynomials, the coefficients being Meixner-Pollaczek type polynomials.
Siddhartha Sahi, Genkai Zhang
doaj
Matrix representation of the time operator
, 2012 In quantum mechanics the time operator $\Theta$ satisfies the commutation relation $[\Theta,H]=i$, and thus it may be thought of as being canonically conjugate to the Hamiltonian $H$.
Arai A. +4 more
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Interpolation of SUSY quantum mechanics [PDF]
, 2007 Interpolation of two adjacent Hamiltonians in SUSY quantum mechanics $H_s=(1-s)A^{\dagger}A + sAA^{\dagger}$, $0\le s\le 1$ is discussed together with related operators.
Andrews G E +7 more
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On the partition function of the six-vertex model with domain wall boundary conditions
, 2004 The six-vertex model on an $N\times N$ square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given.
A G Pronko +29 more
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Ordered Products, $W_{\infty}$-Algebra, and Two-Variable, Definite-Parity, Orthogonal Polynomials
, 1997 It has been shown that the Cartan subalgebra of $W_{\infty}$- algebra is the space of the two-variable, definite-parity polynomials. Explicit expressions of these polynomials, and their basic properties are presented.
Verçin, A.
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Realizations of $su(1,1)$ and $U_q(su(1,1))$ and generating functions for orthogonal polynomials
, 1998 Positive discrete series representations of the Lie algebra $su(1,1)$ and the quantum algebra $U_q(su(1,1))$ are considered. The diagonalization of a self-adjoint operator (the Hamiltonian) in these representations and in tensor products of such ...
Jagannathan, R., Van der Jeugt, J.
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New proofs of determinant evaluations related to plane partitions
, 2012 We give a new proof of a determinant evaluation due to Andrews, which has been used to enumerate cyclically symmetric and descending plane partitions.
Rosengren, Hjalmar
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Mellin transforms with only critical zeros: generalized Hermite functions [PDF]
, 2013 We consider the Mellin transforms of certain generalized Hermite functions based upon certain generalized Hermite polynomials, characterized by a parameter $\mu>-1/2$.
Coffey, Mark W.
core
L2 series solutions of the Dirac equation for power-law potentials at rest mass energy
, 2004 We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. These are written in terms of the confluent hypergeometric function and chosen such that
A D Alhaidari +34 more
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations
, 1996 The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap coefficients in the positive discrete series representations of the Lie algebra su(1,1) and the Clebsch-Gordan decomposition leads to generalisations of the ...
Koelink, H. T., Van der Jeugt, J.
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